The relevant information is: The name of the band derives from Bastille Day, which is celebrated on 14 July, the date of Smith's birthday.
This justifies what answer for what question? Q & A: 
Passage: Bastille (stylised as BΔSTILLE) are a British rock band formed in 2010. The group began as a solo project by lead vocalist Dan Smith, but later expanded to include keyboardist Kyle Simmons, bassist and guitarist Will Farquarson, and drummer Chris Wood. The name of the band derives from Bastille Day, which is celebrated on 14 July, the date of Smith's birthday.

Question: Based on this passage, where did the band bastille get their name?
from Bastille Day , which is celebrated on 14 July , the date of Smith 's birthday